Number of electrons with l = 2 and s = 1/2 in zinc atom

When determining the number of electrons with specific quantum numbers in an atom, we need to consider the electron configuration and the Pauli exclusion principle. In the case of the zinc atom, we can determine the number of electrons with l = 2 and s = 1/2 by following these steps:

1. Determine the electron configuration of zinc:
The electron configuration of zinc is [Ar] 3d10 4s2. This means that the atomic number of zinc is 30, and it has a total of 30 electrons distributed among its energy levels.

2. Determine the number of electrons with l = 2:
The quantum number l represents the azimuthal quantum number, which indicates the shape of the electron's orbital. For l = 2, the possible values for the magnetic quantum number (mℓ) are -2, -1, 0, 1, and 2. Each value of mℓ corresponds to an orbital within the l = 2 subshell, also known as the d subshell.

In the case of zinc, the d subshell is completely filled with 10 electrons (3d10). Therefore, there are no available orbitals with l = 2 in the zinc atom.

3. Determine the number of electrons with s = 1/2:
The quantum number s represents the spin quantum number, which indicates the spin orientation of the electron within its orbital. The possible values for s are +1/2 and -1/2, representing the two possible spin orientations.

In the case of zinc, we need to consider the 4s and 3d subshells. The 4s subshell is partially filled with 2 electrons, which have a spin of +1/2 and -1/2. The 3d subshell is completely filled with 10 electrons, which also have a spin of +1/2 and -1/2.

Therefore, the total number of electrons with s = 1/2 in the zinc atom is 2 + 10 = 12.

Conclusion:
Based on the electron configuration of the zinc atom, the number of electrons with l = 2 and s = 1/2 is 0. However, the total number of electrons with s = 1/2 in the zinc atom is 12.